The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44.

Cover -- Title -- Copyright -- Contents -- 1 Introduction -- 2 Clifford Algebras and Spin Groups -- 2.1 The Clifford Algebras -- 2.2 The groups Pin(V) and Spin(V) -- 2.3 Splitting of the Clifford Algebra -- 2.4 The complexification of the Cl(V) -- 2.5 The Complex Spin Representation -- 2.6 The Group Spin^c(V) -- 3 Spin Bundles and the Dirac Operator -- 3.1 Spin Bundles and Clifford Bundles -- 3.2 Connections and Curvature -- 3.3 The Dirac Operator -- 3.4 The Case of Complex Manifolds -- 4 The Seiberg-Witten Moduli Space -- 4.1 The Equations -- 4.2 Space of Configurations -- 4.3 Group of Changes of Gauge -- 4.4 The Action -- 4.5 The Quotient Space -- 4.6 The Elliptic Complex -- 5 Curvature Identities and Bounds -- 5.1 Curvature Identities -- 5.2 A Priori bounds -- 5.3 The Compactness of the Moduli Space -- 6 The Seiberg-Witten Invariant -- 6.1 The Statement -- 6.2 The Parametrized Moduli Space -- 6.3 Reducible Solutions -- 6.4 Compactness of the Perturbed Moduli Space -- 6.5 Variation of the Metric and Self-dual Two-form -- 6.6 Orientability of the Moduli Space -- 6.7 The Case when b^+2(X) &gt -- 1 -- 6.8 An Involution in the Theory -- 6.9 The Case when b^+2(X) = 1 -- 7 Invariants of Kähler Surfaces -- 7.1 The Equations over a Kähler Manifold -- 7.2 Holomorphic Description of the Moduli Space -- 7.3 Evaluation for Kähler Surfaces -- 7.4 Computation for Kähler Surfaces -- 7.5 Final Remarks -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.